# HONEM: Learning Embedding for Higher Order Networks

## TL;DR

HONEM is a novel embedding method that captures non-Markovian higher-order dependencies in networks, improving performance in various learning tasks over traditional first-order methods.

## Contribution

This paper introduces HONEM, the first embedding approach specifically designed for higher-order networks that accounts for complex dependencies beyond pairwise interactions.

## Key findings

- HONEM outperforms existing methods in node classification.
- HONEM improves network reconstruction accuracy.
- HONEM enhances link prediction and visualization tasks.

## Abstract

Representation learning on networks offers a powerful alternative to the oft painstaking process of manual feature engineering, and as a result, has enjoyed considerable success in recent years. However, all the existing representation learning methods are based on the first-order network (FON), that is, the network that only captures the pairwise interactions between the nodes. As a result, these methods may fail to incorporate non-Markovian higher-order dependencies in the network. Thus, the embeddings that are generated may not accurately represent of the underlying phenomena in a network, resulting in inferior performance in different inductive or transductive learning tasks. To address this challenge, this paper presents HONEM, a higher-order network embedding method that captures the non-Markovian higher-order dependencies in a network. HONEM is specifically designed for the higher-order network structure (HON) and outperforms other state-of-the-art methods in node classification, network re-construction, link prediction, and visualization for networks that contain non-Markovian higher-order dependencies.